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President Barack Obama held a news conference before leaving the climate change conference in Paris

He called on the decisions and goals made at the summit to be 'legally binding'

Republicans in Congress and on the campaign trail remind Obama that his climate actions could be reversed in future years

Paris (CNN)President Barack Obama has long made clear he wants action on climate change to be part of his legacy, and Tuesday in Paris he raised the stakes.

A successful outcome for the United Nations climate talks will include a "legally binding" mechanism to ensure countries adhere to their carbon reduction commitments, Obama said at a press conference before heading back to Washington.

The President listed several criteria for a potential agreement, including an "ambitious target" to reduce carbon output and a slate of tools to measure countries' progress. He said negotiators should insist upon "a single transparency mechanism that all countries are adhering to" and said those mechanisms must be "legally binding."

The nature of the Paris accord has been in dispute, since a legally binding pact — if considered a treaty — would require congressional approval, which he isn't going to get.

To hammer that point, the Republican-controlled House of Representatives on Tuesday afternoon voted to block the Environmental Protection Agency's new limits on carbon dioxide emissions from power plants. Obama will veto the measures, but the timing is no accident -- the GOP is reminding the world the President is in this alone and things could change next November.

"But even if somebody from a different party succeeded me, one of the things you find is when you're in this job, you think about it differently than if you're just running for the job," he said. "American leadership involves not just playing to American constituency back home but you now are in fact at the center of what happens around the world. And that your credibility and America's ability to influence events depends on taking seriously what other countries care about."

"So whoever is the next president of the United States, if they come in and they suggest somehow that that global consensus, not just 99.5% of scientists and experts, but 99% of world leaders think this is really important, I think the President of the United States is going to need to think this is really important," Obama added.

Tell that to Republicans, who have consistently fought Obama's environmental agenda since 2009 and count climate skeptics in key congressional posts -- including Senate Environment and Public Works Chairman Jim Inhofe and House Science Committee Chairman Lamar Smith.

In addition to the House vote on EPA regulations, and threats to block additional climate-related funding, the Science panel is holding a hearing Tuesday: "Pitfalls of Unilateral Negotiations at the Paris Climate Change Conference." Smith is also investigating a key federal study from earlier this year that refuted claims global warming has "paused" over the past two decades -- a study timed conveniently, Smith says, for Obama's climate agenda.

On the campaign trail

GOP presidential candidates have made an applause line by saying Obama's focus on climate change as a top world issue is misplaced.

"I think one of the dumbest statements I've ever heard in politics -- in the history of politics as I know it, which is pretty good, was Obama's statement that our No. 1 problem is global warming," GOP frontrunner Donald Trump said Monday on MSNBC's "Morning Joe."

"I think it's one of the dumbest things I've ever seen, or perhaps most naïve," Trump said. "He actually is somewhat naïve, if you want to know the truth, beyond the incompetent part."

And former Florida Gov. Jeb Bush cited potential economic impacts of environmental regulations as a reason why he would have considered skipping Paris were he currently president.

"I'm not sure I would have gone to the climate summit if I was president today," Bush told reporters in Waterloo, Iowa.

"I worry about the economic impact for our country," Bush said. "I worry that, put aside intentions, that this, these proposals could have an impact on the here and now, on people that are really struggling right now. So I'd be uncertain whether I'd attend a meeting like that, where it seems like the movement is towards policies that would hurt our economy."

As the White House often says when Obama is traveling or when multiple major issues hit the scene simultaneously, the President stressed it's possible to do more than one thing at a time.

"Great nations can handle a lot at once," Obama said. "America's already leading on many issues and climate is no different."

"I know some have asked why the world would dedicate some of our focus right now to combating climate change-- even as we work to protect our people and go after terrorist networks," Obama said. "The reason is because this one trend, climate change, affects all trends. If we let the world keep warming as fast as it is, and sea levels rising as fast as they are, and weather patterns keep shifting in more unexpected ways, then before long we are going to have to devote more and more and more of our economic and military resources not to growing opportunity for our people but to adapting to the various consequences of a changing planet."

Will Paris be successful?

Unlike the 2009 Copenhagen talks widely seen as a failure, Obama and other world leaders visited Paris at the beginning of the U.N. conference, rather than at the end, helping to build momentum for a deal rather than setting up an expectation the leaders would swoop in at the end.

Photos:Marching against global warming

Photos:Marching against global warming

Climate activists organized a silent march in Paris on Sunday to avoid defying a ban on mass protest on Sunday, November 29. More than 140 world leaders are gathering in Paris for high-stakes climate talks that start Monday, and activists are holding marches and protests around the world to urge them to reach a strong agreement to slow global warming.

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Police fight with activists during a protest ahead of the 2015 Paris Climate Conference at the Place de la République.

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A man is detained November 29 by police at the Place de la République, where the candles and flowers were set in memory of the victims of the Paris terror attacks earlier in the month.

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Hundreds of pairs of shoes are displayed at the Place de la République.

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Women dressed as angels pose at the Place de la République.

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Climate change demonstrators march to demand curbs to carbon pollution in London.

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Protesters march down Piccadilly during the London demonstration.

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Climate activists march in front of the Brandenburger Tor in Berlin.

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Activists of the World Wildlife Fund wearing endangered species costumes perform at the Revolution Monument in Mexico City.

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People take part in the Global Climate March in Bogota, Colombia.

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A woman holds a sign reading "No more plastic bags" during a march in Santiago, Chile.

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Climate march participants gather in front of the Helsinki Cathedral in Helsinki, Finland.

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People hold flags and placards while marching in Amsterdam.

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Protesters wearing penguin costumes march in Vienna, Austria.

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People dressed in white crowd form a human glacier in Munich, Germany.

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People form a human chain in Nantes, France.

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Some 700 people from different climate justice movements gather in the Johannesburg, South Africa, focusing on the continued reliance of coal as a primary source of generating electricity.

A protester dressed as a panda bear marches with others holding banners reading "stop climate change" through the streets of central Madrid, Spain.

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Environmental activists march in Seoul, South Korea.

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Obama predicted the inevitable ups and downs of the climate talks.

"I'm sure there will be moments over the next two weeks where progress seems stymied and everyone rushes to write that we are doomed," he said. "But I am convinced that we are going to get big things done here. Keep in mind nobody expected that 180 countries would show up in Paris with serious climate targets in hand."

At his press conference, the President got wonky, noting the goal of seeking to cut the increase in global temperatures to 2 degrees Celsius, although the current commitments from world leaders would still result in a 2.7 degree increase.